{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Math explanation of diffusion models"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forward diffusion process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Quote from paper:\n",
    "What distinguishes diffusion models from other types of latent variable models is that the approximate posterior $q(x_{1:T} |x_0)$, called the forward process or diffusion process, is fixed to a Markov chain that gradually adds Gaussian noise to the data according to a variance schedule β1 , . . . , βT:\n",
    "\n",
    "$q(x_{1:T} |x_0) := \\prod_{t=1}^n q(x_t|x_t−1)$ <br/>\n",
    "$q(x_t|x_{t−1}) := \\mathcal{N}(x_t, \\sqrt{1 − β_t}x_{t−1}, β_tI)$\n",
    "\n",
    "Let's implement the process above in Python"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "import math\n",
    "import numpy as np\n",
    "import src.utils"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Implement q function with 1 dimensional argument\n",
    "# We have to fix a seed to get the same results\n",
    "\n",
    "# Fix a seed to get the same results\n",
    "utils.seed_everything(1000)\n",
    "\n",
    "# Number of timesteps\n",
    "timestep = 800\n",
    "\n",
    "# Our interval\n",
    "xs = np.arange(-5, 5, 0.01)\n",
    "\n",
    "# Apply normal pdf to xs with 0 mean and 1 variance (Just to check graph with our graphs)\n",
    "y_results = norm.pdf(xs, 0, 1)\n",
    "\n",
    "different_schedules = [\n",
    "    # constant\n",
    "    np.ones(timestep) * 0.1,\n",
    "    np.ones(timestep) * 0.3,\n",
    "    np.ones(timestep) * 0.5,\n",
    "    np.ones(timestep) * 0.7,\n",
    "    np.ones(timestep) * 0.9,\n",
    "    # linear change (from paper)\n",
    "    np.linspace(1e-4, 0.02, timestep)\n",
    "]\n",
    "\n",
    "# set x0 some random value from -1 to 1\n",
    "x0 = 3\n",
    "\n",
    "for bt in different_schedules:\n",
    "\n",
    "    # Set xt to zero, which will be used as x(t-1) like in sqrt(1-b) * x(t-1)\n",
    "    xt = x0\n",
    "\n",
    "    q_results = None\n",
    "\n",
    "    # A simple loop by timestep\n",
    "    for t in range(timestep):\n",
    "\n",
    "        # Calculate the mean as in the formula\n",
    "        mean = math.sqrt(1 - bt[t]) * xt\n",
    "\n",
    "        # Calculate the variance\n",
    "        variance = bt[t]\n",
    "\n",
    "        # Q is a normal distribution, so to get the next xt, we just get random element from our distribution\n",
    "        xt = np.random.normal(mean, math.sqrt(variance))\n",
    "    q_results = norm.pdf(xs, mean, math.sqrt(variance))\n",
    "    plt.plot(xs, q_results, label=f\"qt for bt {bt[0] if bt[0] == bt[-1] else 'linear'}\")\n",
    "plt.plot(xs, y_results, label=\"Y\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In previous code we have a line:\n",
    "\n",
    "```python\n",
    "xt = np.random.normal(mean, math.sqrt(variance))\n",
    "```\n",
    "\n",
    "It means we always get some random variable. If we want to make a backpropagation in the future, it's hard to do it, because we can not make deriviative $x_t$ by $x_{t-1}$.\n",
    "To avoid this situation lets make a reparametrization trick.\n",
    "\n",
    "$x_t \\sim q(x_t | x_{t-1}) := \\mathcal{N}(x_t, \\mu_{t-1}, \\delta_{t-1} ^2 ) $ <br/>\n",
    "$x_t = \\mu_{t-1} + \\delta_{t-1} * \\epsilon$, where $\\epsilon \\sim \\mathcal{N}(0, I)$\n",
    "\n",
    "For our case we have:\n",
    "\n",
    "$x_t = \\sqrt{1 - \\beta_t}x_{t-1} + \\beta_t * \\epsilon$, where $\\epsilon \\sim \\mathcal{N}(0, I)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fixed seed to get the same results\n",
    "utils.seed_everything(1000)\n",
    "\n",
    "for bt in different_schedules:\n",
    "\n",
    "    # Set xt to zero, which will be used as x(t-1) like in sqrt(1-b) * x(t-1)\n",
    "    xt = x0\n",
    "\n",
    "    q_results = None\n",
    "\n",
    "    # A simple loop by timestep\n",
    "    for t in range(timestep):\n",
    "\n",
    "        # Calculate the mean as in the formula\n",
    "        mean = math.sqrt(1 - bt[t]) * xt\n",
    "\n",
    "        # Calculate the variance\n",
    "        variance = math.sqrt(bt[t])\n",
    "\n",
    "        # Get eps from normal distribution\n",
    "        eps = np.random.normal(0, 1)\n",
    "        \n",
    "        # Calculate our xt\n",
    "        xt = mean + variance * eps\n",
    "    q_results = norm.pdf(xs, mean, math.sqrt(variance))\n",
    "    plt.plot(xs, q_results, label=f\"qt for bt {bt[0] if bt[0] == bt[-1] else 'linear'}\")\n",
    "plt.plot(xs, y_results, label=\"Y\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see first two methods leads us to normal distribution in the end for all beta schedules.\n",
    "\n",
    "Right now we have a direct formula to compute $x_t$. When we are working in one dimensional, it's so easy and fast to compute $x_t$, but if we want to work in 100D, 1000D, 10000D, etc. our loop will be a big pain and have a bad performance.\n",
    "\n",
    "Can we avoid our timestep loop? Let's go to formulas\n",
    "\n",
    "$\\alpha_t = 1 - \\beta_t, \\bar \\alpha_t = \\prod_{i=1}^t\\alpha_i$ <br/>\n",
    "$x_t = \\sqrt{\\alpha_t}x_{t-1} + \\sqrt{1 - \\alpha_t} * \\epsilon_t = \\sqrt{\\alpha_t} \\sqrt{\\alpha_{t-1}} x_{t-2} + \\sqrt{\\alpha_t * (1 - \\alpha_{t-1})} * \\epsilon_{t-1} + \\sqrt{1 - \\alpha_t} * \\epsilon_t$\n",
    "\n",
    "$\\epsilon_t \\sim \\mathcal{N}(0, \\delta_t^2 I)$ and $\\epsilon_{t-1} \\sim \\mathcal{N}(0, \\delta_{t-1}^2 I)$. So their merge will be $\\mathcal{N}(0, (\\delta_t^2 + \\delta_{t-1}^2)I)$. Rewrite the formula above:\n",
    "\n",
    "$x_t=\\sqrt{\\alpha_t * \\alpha_{t-1}} x_{t-2} + \\sqrt{\\alpha_t * (1 - \\alpha_{t-1}) + 1 - \\alpha_t} * \\bar{\\epsilon_{t-2}} = \\sqrt{\\alpha_t * \\alpha_{t-1}} x_{t-2} + \\sqrt{1 - \\alpha_t * \\alpha_{t-1}} * \\bar{\\epsilon_{t-2}}$ <br/>\n",
    "\n",
    "And then we can continue this line until we reach x0: <br/>\n",
    "$x_t=\\sqrt{\\bar \\alpha_t} x_0 + \\sqrt{1 - \\bar \\alpha_t} * \\bar{\\epsilon}$\n",
    "\n",
    "Lets try to implement it and compare results with previous graphs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Fixed seed to get the same results\n",
    "utils.seed_everything(1000)\n",
    "\n",
    "for bt in different_schedules:\n",
    "    alpha_t = 1 - bt\n",
    "    cumprod_alpha_t = np.cumprod(alpha_t)\n",
    "    mean = math.sqrt(cumprod_alpha_t[-1]) * x0\n",
    "    variance = math.sqrt(1 - cumprod_alpha_t[-1])\n",
    "    eps = np.random.normal(0, 1)\n",
    "    variance = variance\n",
    "    xt = mean + eps * variance\n",
    "    q_results = norm.pdf(xs, mean, math.sqrt(variance))\n",
    "    plt.plot(xs, q_results, label=f\"qt for bt {bt[0] if bt[0] == bt[-1] else 'linear'}\")\n",
    "plt.plot(xs, y_results, label=\"Y\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we can see the last method take us closer to Normal distribution with zero mean and one variance.\n",
    "So, now we have transformation of a point(point will be an image) to point from Normal distribution(image with a noise)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Reverse diffusion process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Problem with the reverse diffusion process"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What about a reverse diffusion process:\n",
    "$q(x_{t-1}|x_t)$ ?\n",
    "\n",
    "As we will see later, we don't have enough data to make this transformation, but we can do something like this:\n",
    "$q(x_{t-1}|x_t, x_0)$\n",
    "\n",
    "**What doest it mean?** We try to find the distribution $x_{t-1}$, knowing distribution $x_t, x_0$.\n",
    "\n",
    "I will provide formulas of this calculation later. But right now the question is: can we draw $q(x_{t-1}|x_t)$ from $q(x_{t-1}|x_t, x_0)$ ?\n",
    "\n",
    "Yes, we just need some formulas from statistic theory ([very good explanation](https://stats.libretexts.org/Courses/Saint_Mary's_College_Notre_Dame/MATH_345__-_Probability_\\(Kuter\\)/1%3A_What_is_Probability)).\n",
    "\n",
    "Let's do some magic.\n",
    "\n",
    "$\\begin{aligned}q(x_{t-1}|x_t, x_0) = \\frac{q(x_{t-1}, x_t, x_0)}{q(x_t, x_0)}\\end{aligned}$ (1)\n",
    "\n",
    "$\\begin{aligned}q(x_{t-1}|x_t)=\\int_{x_0} q(x_{t-1}, x_0|x_t) \\mathrm{d}x_0\\end{aligned}$ (2)\n",
    "\n",
    "$\\begin{aligned}q(x_{t-1}, x_0| x_t) = \\frac{q(x_{t-1}, x_0, x_t)}{q(x_t)} \\end{aligned}$ (3)\n",
    "\n",
    "Drawing numerator from (1) and (3) and assining them to each other, we have <br/><br/>\n",
    "$\\begin{aligned} q(x_{t-1}|x_t, x_0) * q(x_t, x_0) = q(x_{t-1}, x_0| x_t) * q(x_t) => q(x_{t-1}, x_0| x_t) = q(x_{t-1}|x_t, x_0) * \\frac{q(x_t, x_0)}{q(x_t)} \\end{aligned}$\n",
    "\n",
    "$\\begin{aligned} q(x_{t-1}, x_0| x_t) = q(x_{t-1}|x_t, x_0) * q(x_0|x_t) \\end{aligned}$\n",
    "\n",
    "And redraw formula (2):\n",
    "$q(x_{t-1}|x_t)=\\int q(x_{t-1}|x_t, x_0) * q(x_0|x_t) \\mathrm{d}x_0$\n",
    "\n",
    "With Bayes formula we can draw $q(x_0|x_t)$ as $\\begin{aligned} q(x_t|x_0) * \\frac{q(x_0)}{q(x_t)} \\end{aligned}$\n",
    "\n",
    "So to calculate $q(x_{t-1}|x_t)$ we should make integral through all $x_0$ (all images in dataset), which means a lot of computations and super slow as the result."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Working with $q(x_{t-1}|x_t, x_0)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First of all, we should say, that if $\\beta$ is small and $q(x_t|x_{t-1})$ is Gaussian, then $q(x_{t-1}|x_t)$ is Gaussian too. A quote from paper:\n",
    "\n",
    "\"For both Gaussian and binomial diffusion, for continuous diffusion (limit of small step size β) the reversal of the diffusion process has the identical functional form as the forward process (Feller, 1949).\"\n",
    "\n",
    "I tried to read Feller original, but it was so hard to understand, so let's take this fact as true.\n",
    "\n",
    "So if it is Gaussian, we should try to find $\\mu$ and $\\delta$ of this Gaussian. Lets do it.\n",
    "\n",
    "Using Bayes' rule we have (took part of calculations from [Lil Log article](https://lilianweng.github.io/posts/2021-07-11-diffusion-models/)): <br/>\n",
    "$\\begin{aligned}q(x_{t-1}|x_t, x_0) = q(x_{t}|x_{t-1},x_0) * \\frac{q(x_{t}|x_0)}{q(x_{t-1}|x_0)}\\end{aligned}$<br/>\n",
    "$\\begin{aligned}\\propto \\exp (-\\frac{1}{2} * (\\frac{(x_t - \\sqrt{\\alpha_t}x_{t-1})^2}{\\beta_t} + \\frac{(x_{t-1} - \\sqrt{\\bar \\alpha_{t-1}}x_0)^2}{1 - \\bar \\alpha_{t-1}} - \\frac{(x_{t} - \\sqrt{\\bar \\alpha_{t}}x_0)^2}{1 - \\bar \\alpha_t})) \\end{aligned}$<br/>\n",
    "$\\begin{aligned}\n",
    "&= \\exp (-\\frac{1}{2} (\\frac{\\mathbf{x}_t^2 - 2\\sqrt{\\alpha_t} \\mathbf{x}_t \\mathbf{x}_{t-1} + \\alpha_t \\mathbf{x}_{t-1}^2 }{\\beta_t} + \\frac{ {\\mathbf{x}_{t-1}^2} {- 2 \\sqrt{\\bar{\\alpha}_{t-1}} \\mathbf{x}_0} {\\mathbf{x}_{t-1}} + \\bar{\\alpha}_{t-1} \\mathbf{x}_0^2}  {1-\\bar{\\alpha}_{t-1}} - \\frac{(\\mathbf{x}_t - \\sqrt{\\bar{\\alpha}_t} \\mathbf{x}_0)^2}{1-\\bar{\\alpha}_t} ) ) \\\\\n",
    "&= \\exp\\Big( -\\frac{1}{2} \\big( {(\\frac{\\alpha_t}{\\beta_t} + \\frac{1}{1 - \\bar{\\alpha}_{t-1}})} \\mathbf{x}_{t-1}^2 - (\\frac{2\\sqrt{\\alpha_t}}{\\beta_t} \\mathbf{x}_t + \\frac{2\\sqrt{\\bar{\\alpha}_{t-1}}}{1 - \\bar{\\alpha}_{t-1}} \\mathbf{x}_0) \\mathbf{x}_{t-1} + C(\\mathbf{x}_t, \\mathbf{x}_0) \\big) \\Big)\n",
    "\\end{aligned}$\n",
    "\n",
    "Just reminder:\n",
    "\n",
    "$\\begin{aligned} N(x, \\mu, \\delta^2) \\sim x \\propto \\exp (-1/2 * \\frac{(x - \\mu) ^ 2}{\\delta^2}) \\end{aligned}$\n",
    "\n",
    "Look detally at:\n",
    "\n",
    "$\\begin{aligned}\\frac{(x - \\mu) ^ 2}{\\delta^2} = \\frac{(x^2 - 2x\\mu + \\mu^2)}{\\delta^2} = \\frac{1}{\\delta^2} * x^2 - 2 * \\frac{\\mu}{\\delta^2} * x + ... \\end{aligned}$\n",
    "\n",
    "If we have $A * x ^ 2$, then $\\delta^2 = 1 / A$. Similar for $\\mu: B * x => \\mu = -\\frac{1}{2} * \\delta^2 * B $\n",
    "\n",
    "Draw our mean and variance for $q(x_{t-1}|x_t, x_0)$\n",
    "\n",
    "$\\begin{aligned} (\\frac{\\alpha_t}{\\beta_t} + \\frac{1}{1 - \\bar{\\alpha}_{t-1}}) \\mathbf{x}_{t-1}^2 => \\delta^2 = 1/A = 1 / (\\frac{\\alpha_t}{\\beta_t} + \\frac{1}{1 - \\bar{\\alpha}_{t-1}}) = \\frac{1 - \\bar \\alpha_{t-1}}{1 - \\bar \\alpha_{t}} \\beta_t \\end{aligned}$\n",
    "\n",
    "\n",
    "$\\begin{aligned} -(\\frac{2\\sqrt{\\alpha_t}}{\\beta_t} \\mathbf{x}_t + \\frac{2\\sqrt{\\bar{\\alpha}_{t-1}}}{1 - \\bar{\\alpha}_{t-1}} \\mathbf{x}_0) \\mathbf{x}_{t-1} => \\mu = -\\frac{1}{2} * \\delta^2 * B = \\frac{\\sqrt{\\alpha_t}(1- \\bar \\alpha_{t-1})}{1 - \\bar \\alpha_t}x_t + \\frac{\\sqrt{\\bar \\alpha_{t-1}} * \\beta_t}{1 - \\bar{\\alpha_{t}}}x_0 \\end{aligned}$\n",
    "\n",
    "Now $q(x_{t-1}|x_t, x_0) \\sim N(x_{t-1}, \\mu(x_t, x_0), \\tilde \\beta_tI)$\n",
    "\n",
    "<a name=\"formula_4\"></a>\n",
    "\n",
    "$\\begin{aligned} \\tilde \\beta_t = \\frac{1 - \\bar \\alpha_{t-1}}{1 - \\bar \\alpha_{t}} \\beta_t \\end{aligned}$ <span style=\"color: blue\"> (4) </span>\n",
    "\n",
    "<a name=\"formula_5\"></a>\n",
    "\n",
    "$\\begin{aligned} \\mu(x_t, x_0) = \\frac{\\sqrt{\\alpha_t}(1- \\bar \\alpha_{t-1})}{1 - \\bar \\alpha_t}x_t + \\frac{\\sqrt{\\bar \\alpha_{t-1}} * \\beta_t}{1 - \\bar{\\alpha_{t}}}x_0 \\end{aligned}$ <span style=\"color: blue\"> (5) </span>\n",
    "\n",
    "Recall that $x_t=\\sqrt{\\bar \\alpha_t} x_0 + \\sqrt{1 - \\bar \\alpha_t} * \\bar{\\epsilon}$, draw $x_0$ through $x_t$\n",
    "\n",
    "$\\begin{aligned}x_0=\\frac{1}{\\sqrt{\\bar \\alpha_t}} (x_t - \\sqrt{1 - \\bar \\alpha_t} * \\bar{\\epsilon}) \\end{aligned}$\n",
    "\n",
    "Next, draw our new $\\tilde \\mu_t$ without $x_0$\n",
    "\n",
    "$\\begin{aligned} \\tilde \\mu_t = \\frac{\\sqrt{\\alpha_t}(1- \\bar \\alpha_{t-1})}{1 - \\bar \\alpha_t}x_t + \\frac{\\sqrt{\\bar \\alpha_{t-1}} * \\beta_t}{(1 - \\bar{\\alpha_{t}})\\sqrt{\\bar \\alpha_t}}(x_t - \\sqrt{1 - \\bar \\alpha_t} * \\bar{\\epsilon})=\\frac{1}{\\sqrt{\\alpha_t}}x_t - \\frac{1}{\\sqrt{\\alpha_t}} * \\frac{\\sqrt{1 - \\bar \\alpha_t}}{1 - \\bar \\alpha_t} * \\beta_t * \\bar {\\epsilon} \\end{aligned}$\n",
    "\n",
    "Recall $\\beta_t = 1 - \\alpha_t$ we have\n",
    "\n",
    "<a name=\"formula_6\"></a>\n",
    "\n",
    "$\\begin{aligned} \\tilde \\mu_t = \\frac{1}{\\sqrt{\\alpha_t}}(x_t - \\frac{1 - \\alpha_t}{\\sqrt{1 - \\bar \\alpha_t}} \\bar {\\epsilon}) \\end{aligned}$ <span style=\"color: blue\"> (6) </span>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Transition from $q(x_{t-1}|x_t)$ to $p_\\theta(x_{t-1}|x_t)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw before, we can not calculate $q(x_{t-1}|x_t)$ , so we introduce a model $p_\\theta(x_{t-1}|x_t)$, which approximate our q.\n",
    "As we discussed earlier $q(x_{t-1}|x_t)$ is Gaussian, so $p_\\theta(x_{t-1}|x_t)$ is Gaussian too. So we have:\n",
    "\n",
    "$p_\\theta(x_{t-1}|x_t) = N(x_{t-1}, \\mu_\\theta(x_t, t), \\Sigma_\\theta(x_t, t)) \\quad p(x_{0...T}) = p(x_{0:T}) = p(x_T) * \\prod_{t=1}^T p_\\theta(x_{t-1}|x_t)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have model $p_\\theta(x_{t-1}|x_t)$, which describes some distribution and we have distribution $q(x_{t-1}|x_t)$ and we want to find optimal $\\theta$, that $p_\\theta$ will be the closest to $q$. It sounds we have to find a loss function.\n",
    "\n",
    "To do this let's write likelihood for $p_\\theta$\n",
    "\n",
    "$p_\\theta(x) = \\int p_\\theta(x_{0:T})\\mathrm{d}x_1,...x_T$`\n",
    "\n",
    "Our goal is to maximize it, write logarithm of likelihood:\n",
    "\n",
    "$\\begin{aligned}\n",
    "\\log p_\\theta(x) &= \\log \\int p_\\theta(x_{0:T})\\mathrm{d}x_1,...x_T \\\\\n",
    "&= \\log \\int p_\\theta(x_{0:T}) * \\frac{q(x_{1:T}|x_0)}{q(x_{1:T}|x_0)}\\mathrm{d}x_1,...x_T \\\\\n",
    "&= \\log \\int q(x_{1:T}|x_0) * \\frac{p_\\theta(x_{0:T})}{q(x_{1:T}|x_0)}\\mathrm{d}x_1,...x_T \\\\\n",
    "&= \\log E_{q(x_{1:T}|x_0)} \\frac{p_\\theta(x_{0:T})}{q(x_{1:T}|x_0)} \\\\\n",
    "\\end{aligned}$\n",
    "\n",
    "Now let's write Jensen’s Inequality:\n",
    "$f(E(x)) <= E(f(x))$, if $f(x)$ is a convex function and $f(E(x)) >= E(f(x))$, if $f(x)$ is a concave.\n",
    "\n",
    "$log(x)$ is a concave, so:\n",
    "$log(E(x)) >= E(log(x))$\n",
    "\n",
    "Rewrite our formula above:\n",
    "\n",
    "$\\begin{aligned}\n",
    "\\log p_\\theta(x) &= \\log E_{q(x_{1:T}|x_0)} \\frac{p_\\theta(x_{0:T})}{q(x_{1:T}|x_0)} \\\\\n",
    "&= E_{q(x_{1:T}|x_0)}[ \\log  \\frac {p_\\theta(x_T) * p_\\theta(x_0|x_1) * \\prod_{t=2}^{T} p_\\theta(x_{t-1}|x_t) } { q(x_1|x_0) * \\prod_{t=2}^{T} q(x_t|x_{t-1}) } ] \\\\\n",
    "&= E_{q(x_{1:T}|x_0)}[ \\log  \\frac {p_\\theta(x_T) * p_\\theta(x_0|x_1) } { q(x_1|x_0) } +\n",
    "\\log \\prod_{t=2}^{T} \\frac { p_\\theta(x_{t-1}|x_t) } { q(x_t|x_{t-1}) } ] \\\\\n",
    "&= E_{q(x_{1:T}|x_0)}[ \\log  \\frac {p_\\theta(x_T) * p_\\theta(x_0|x_1) } { q(x_1|x_0) } +\n",
    "\\log \\prod_{t=2}^{T} \\frac { p_\\theta(x_{t-1}|x_t) } { \\frac { q(x_{t-1}|x_t, x_0) * \\cancel { q(x_t|x_0) } } { \\cancel { q(x_{t-1} | x_0) } } } ] \\\\\n",
    "&= E_{q(x_{1:T}|x_0)}[ \\log  \\frac {p_\\theta(x_T) * p_\\theta(x_0|x_1) } { q(x_1|x_0) } +\n",
    "\\log  \\frac {q_(x_1|x_0) } { q(x_T|x_0) } +\n",
    "\\log \\prod_{t=2}^{T} \\frac { p_\\theta(x_{t-1}|x_t) } { q(x_{t-1}|x_t, x_0) } ] \\\\\n",
    "&= E_{q(x_{1:T}|x_0)}[ \\log \\frac{p_\\theta(x_T) * p_\\theta(x_0|x_1)}{q(x_T|x_0) }] +\n",
    "E_{q(x_{1:T}|x_0)}[ \\log  \\prod_{t=2}^{T} \\frac {p_\\theta(x_{t-1}|x_{t})}{q(x_{t-1}|x_{t}, x_0)} ] \\\\\n",
    "&= E_{q(x_{1:T}|x_0)} \\log p_\\theta(x_0|x_1) +\n",
    "E_{q(x_{1:T}|x_0)} \\log \\frac{p_\\theta(x_T)}{q(x_T|x_{0}) } +\n",
    "E_{q(x_{1:T}|x_0)}[ \\sum_{t=2}^{T} \\log  \\frac {p_\\theta(x_{t - 1}|x_{t})}{q(x_{t-1}|x_{t},x_0)} ] \\\\\n",
    "&= E_{q(x_1|x_0)} \\log p_\\theta(x_0|x_1) +\n",
    "E_{q(x_T|x_0)} \\log \\frac{p_\\theta(x_T)}{q(x_T|x_0) } +\n",
    "\\sum_{t=2}^{T} [E_{q(x_{t-1},x_t|x_0)} \\log  \\frac {p_\\theta(x_{t-1}|x_{t})}{q(x_{t-1}|x_{t},x_0)} ] \\\\\n",
    "&= E_{q(x_1|x_0)} \\log p_\\theta(x_0|x_1) -\n",
    "D_{KL} (q(x_T|x_0) || p_\\theta(x_T)) -\n",
    "\\sum_{t=2}^{T} [E_{q(x_{t-1}|x_0)} D_{KL} (q(x_{t-1}|x_t, x_0) || p_\\theta(x_{t-1}|x_t)) ]\n",
    "\\end{aligned}$\n",
    "\n",
    "$\\log p_\\theta(x) >= E_{q(x_1|x_0)} \\log p_\\theta(x_0|x_1) -\n",
    "D_{KL} (q(x_T|x_0) || p_\\theta(x_T)) -\n",
    "\\sum_{t=2}^{T} [E_{q(x_{t-1}|x_0)} D_{KL} (q(x_{t-1}|x_t, x_0) || p_\\theta(x_{t-1}|x_t)) ]$ <span style=\"color: blue\"> (7) </span>\n",
    "\n",
    "Name of the formula above is Evidence Lower Bound (ELBO). And special thanks to Calvin Luo with his great [article](https://calvinyluo.com/2022/08/26/diffusion-tutorial.html#mjx-eqn%3Aeq%3A79) with explanations of math."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the formula above the first statement E(q) and second statement don't depend on $p_\\theta(x_{t-1}|x_t)$, so we can skip them and work only with the last statement.\n",
    "Our goal is to maximize log likelihood, so from [formula 6](#formula_6) we should to minimize $\\sum_{t=2}^{T} [E_{q(x_{t-1}|x_0)} D_{KL} (q(x_{t-1}|x_t, x_0) || p_\\theta(x_{t-1}|x_t)) ]$\n",
    "\n",
    "$D_{KL}$ is always positive, our goal is to minimize it.\n",
    "\n",
    "It seems we found our loss function. Couple words about Kullback–Leibler divergence.\n",
    "\n",
    "KL Divergence or $D_{KL}(P||Q)$ shows how probability distribution P differs from another probability distribution Q. If P and Q equal, then $D_{KL} = 0$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1800x800 with 6 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show KL divergence on sample with two Gaussians\n",
    "\n",
    "# Fix a seed to get the same results\n",
    "utils.seed_everything(1000)\n",
    "\n",
    "# Our interval\n",
    "xs = np.arange(-20, 20, 0.01)\n",
    "\n",
    "# Let q will be gaussian with mean=2 and variance=4\n",
    "q_results = norm.pdf(xs, 2, 4)\n",
    "\n",
    "thetas = [(0.1, 10), (1, 8), (2, 1), (2,5), (3, 4), (5, 7)]\n",
    "\n",
    "cols = 3\n",
    "rows = len(thetas) // cols\n",
    "\n",
    "fig, axs = plt.subplots(rows, cols, figsize=(6 * cols, 4 * rows))\n",
    "\n",
    "for index, theta in enumerate(thetas):\n",
    "    p_results = norm.pdf(xs, theta[0], theta[1])\n",
    "    axs_index = (index // cols, index % cols)\n",
    "    axs[axs_index].plot(xs, q_results, label=f\"Q(2,4)\")\n",
    "    axs[axs_index].plot(xs, p_results, label=f\"P({theta[0]}, {theta[1]})\")\n",
    "    div_PQ = np.sum(p_results * np.log(p_results / q_results))\n",
    "    div_QP = np.sum(q_results * np.log(q_results / p_results))\n",
    "    axs[axs_index].set_title(f\"KL(Q|P) divergence is {div_PQ:.2f}, KL(P|Q) divergence is {div_QP:.2f}\")\n",
    "    axs[axs_index].legend()\n",
    "# plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Loss function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is the fact that [KL Divergence between two Gaussian distributions](https://en.wikipedia.org/wiki/Kullback%E2%80%93Leibler_divergence#Multivariate_normal_distributions) with the same dimension k is:\n",
    "\n",
    "$\\begin{aligned} N_0(\\mu_0, \\Sigma_0); \\: N_1(\\mu_1, \\Sigma_1); \\; D_{KL}(N_0 || N_1) = \\frac{1}{2}(tr(\\Sigma_1^{-1}\\Sigma_0) - k + (\\mu_1 - \\mu_0)^T\\Sigma_1^{-1}(\\mu_1 - \\mu_0) + ln \\frac{det\\Sigma_1}{det\\Sigma_0}) \\end{aligned}$\n",
    "\n",
    "Recall that $p_{theta} \\sim N(\\mu_{\\theta}(x_t, t), \\sigma_{\\theta}(x_t, t)); \\ q(x_{t-1}|x_t, x_0) \\sim N(x_t, \\mu(x_t, x_0), \\sigma(t))$\n",
    "\n",
    "Draw $D_{KL} (q(x_{t-1}|x_t, x_0) || p_\\theta(x_{t-1}|x_t))$\n",
    "\n",
    "$\\begin{aligned}\n",
    "D_{KL} (q(x_{t-1}|x_t, x_0) || p_\\theta(x_{t-1}|x_t))\n",
    "&= \\frac{1}{2}(k-k + (\\mu(x_t, x_0) - \\mu_{\\theta}(x_t, t)) \\Sigma_1^{-1}(\\mu(x_t, x_0) - \\mu_{\\theta}(x_t, t)) + ln1) \\\\\n",
    "&= \\frac{1}{2}(\\mu(x_t, x_0) - \\mu_{\\theta}(x_t, t))\\frac{1}{\\sigma_q^2(t)}(\\mu(x_t, x_0) - \\mu_{\\theta}(x_t, t)) \\\\\n",
    "&= \\frac{1}{2\\sigma_q^2(t)} ||\\mu(x_t, x_0) - \\mu_{\\theta}(x_t, t)||_2^2\n",
    "\\end{aligned}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Take formula <span style=\"color: blue\">(5)</span> and wewrite it:\n",
    "\n",
    "$\\begin{aligned}\n",
    "\\mu(x_t, x_0)=\\frac{\\sqrt{\\alpha_t}(1- \\bar \\alpha_{t-1})}{1 - \\bar \\alpha_t}x_t + \\frac{\\sqrt{\\bar \\alpha_{t-1}} * \\beta_t}{1 - \\bar{\\alpha_{t}}}x_0 \\\\\n",
    "\\mu_\\theta(x_t, t)=\\frac{\\sqrt{\\alpha_t}(1- \\bar \\alpha_{t-1})}{1 - \\bar \\alpha_t}x_t + \\frac{\\sqrt{\\bar \\alpha_{t-1}} * \\beta_t}{1 - \\bar{\\alpha_{t}}}x_{\\theta} \\\\\n",
    "D_{KL} = \\frac{1}{2\\sigma_q^2(t)} * \\frac{\\bar \\alpha_{t-1} * (1 - \\alpha_t)^2}{(1 - \\bar{\\alpha_{t}})^2} ||x_0 - x_{\\theta}||_2^2\n",
    "\\end{aligned}$\n",
    "\n",
    "Where $x_{\\theta}$ - predicted image from our neural network.\n",
    "\n",
    "Take formula <span style=\"color: blue\">(6)</span> and wewrite it too:\n",
    "\n",
    "$\\begin{aligned}\n",
    "\\tilde \\mu_t(x_t) = \\frac{1}{\\sqrt{\\alpha_t}}(x_t - \\frac{1 - \\alpha_t}{\\sqrt{1 - \\bar \\alpha_t}} \\bar {\\epsilon}) \\\\\n",
    "\\tilde \\mu_{\\theta}(x_t) = \\frac{1}{\\sqrt{\\alpha_t}}(x_t - \\frac{1 - \\alpha_t}{\\sqrt{1 - \\bar \\alpha_t}} \\epsilon_{\\theta}) \\\\\n",
    "D_{KL} = \\frac{1}{2\\sigma_q^2(t)} * \\frac{(1 - \\alpha_t)^2}{\\alpha_t (1 - \\bar{\\alpha_{t}})} ||\\epsilon - \\epsilon_{\\theta}||_2^2\n",
    "\\end{aligned}$\n",
    "\n",
    "Where $\\epsilon$ - noise, which we added to the image, $\\epsilon_{\\theta}$ - predicted noise from our neural network.\n",
    "\n",
    "So now loss will look like:\n",
    "\n",
    "$\\begin{aligned}\n",
    "Loss(\\theta) = \\arg \\min_{\\theta} \\sum_{t=2}^{T}E_{q(x_t|x_0)} [\\ \\frac{1}{2\\sigma_q^2(t)} * \\frac{(1 - \\alpha_t)^2}{\\alpha_t (1 - \\bar{\\alpha_{t}})} ||\\epsilon - \\epsilon_{\\theta}||_2^2 \\ ]\n",
    "\\end{aligned}$\n",
    "\n",
    "But it's better to use simple form of it:\n",
    "\n",
    "$\\begin{aligned}\n",
    "Loss_{simple}(\\theta) = \\arg \\min_{\\theta} \\sum_{t=2}^{T}E_{q(x_t|x_0)} ||\\epsilon - \\epsilon_{\\theta}||_2^2\n",
    "\\end{aligned}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## How to get a sample"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recall $p_\\theta(x_{t-1}|x_t) = \\N(x_t, \\mu_\\theta(x_t), \\Sigma_\\theta(x_t, t))$ and $\\Sigma_\\theta = \\beta_t$ in our case, so we have:\n",
    "\n",
    "$\\begin{aligned}\n",
    "x_{t-1} &= \\mu_\\theta(x_t) + \\epsilon * \\Sigma_\\theta, \\epsilon \\sim \\N(0, I) \\\\\n",
    "&= \\frac{1}{\\sqrt{\\alpha_t}}(x_t - \\frac{1 - \\alpha_t}{\\sqrt{1 - \\bar \\alpha_t}} \\bar {\\epsilon}) + \\epsilon * \\beta_t\n",
    "\\end{aligned}$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Results"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We did a lot of calculations and as the result we have a real simple loss as distance between real noise (which will be added to an image) and predicted noise from neural network"
   ]
  }
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